• Unit 5: Rotational Kinematics

Now that we have discussed forces and how they manipulate motion, we will begin exploring a particular force that makes objects move in a curved motion. In this unit, we study the simplest form of curved motion: uniform circular motion, or motion in a circular path at a constant speed. In some ways, this unit is a continuation of the previous unit on dynamics, but we will introduce new concepts such as angular velocity and acceleration, centripetal force, and the force of gravity.

Completing this unit should take you approximately 3 hours.

• 5.1: Centripetal Force

A centripetal force is any force that makes an object move in a circular motion. A centripetal force can involve any of the classical or electromagnetic forces, such as gravitational force (weight), normal force, tension, and friction.

For example, gravitational force acts as a centripetal force on a planetary scale because it causes planets to orbit in a circle. However, gravitational force is not a centripetal force on the Earth's surface because gravity makes objects fall straight down toward the Earth's center, not in a circle. A normal force can act as a centripetal force, such when a roller coaster does a loop-da-loop. Friction can act as a centripetal force, such as when it causes cars to turn corners on a road.

The equation for centripetal acceleration is $a_c=\frac{v^2}{r}$, where $v$ is object speed and $r$ is radius (distance from center).

• 5.2: Centripetal Force and the Universal Law of Gravitation

A dramatic application of centripetal force is the Universal Law of Gravitation. Johannes Kepler (1571–1630), the German astronomer and mathematician, created three laws that pertain to orbital motion during the Renaissance period. At this time, physics and astronomy were two separate fields of study. Kepler developed these three laws independently from the laws of physics we know today.

• 5.3: Angular Position, Velocity, and Acceleration

In rotational motion, we deal with two-dimensional motion. Unlike with linear motion, we need to define angles and distances associated with circular motion.

• 5.4: Kinematics of Rotational Motion

Rotational Kinematics is the study of rotational motion, much like linear kinematics (or just plain kinematics) is the study of linear motion. When solving kinematics problems of rotational motion, we look at the relationships between angular and linear versions of position, velocity, and acceleration.